报告题目：Modeling, Analysis and Simulation of Flows in Karstic Geometry
报 告 人：Prof. Xiaoming Wang, Ph.D
Xiaoming Wang，美国佛罗里达州立大学(Florida State University)数学系主任、教授、博士生导师，地球物理流体动力学研究所研究员。曾在美国纽约大学库朗数学研究所工作。目前受聘为复旦大学数学学院客座教授。主要从事流体动力学、地下水动力学以及紊流研究。
Karst geometry is a particular type of configuration that consists of both conduit/channel (or vug/chamber) together with porous media. Many important applications involve fluid flows in karstic geometry. Well-known examples include contaminant transport in karst aquifers, oil recovery in karst oil reservoirs, proton exchange membrane fuel cell technology, cardiovascular modeling, and carbon-dioxide sequestration among others. The mathematical study of flows in karstic geometry is a challenge due to the coupling of the flows in the conduits and the surrounding matrix, which are governed by different physical processes, the possibly complex geometry of the network of conduits, the vastly disparate spatial and temporal scales, the strong heterogeneity and enormous associated uncertainty in natural karst aquifers, and the multiphase nature of many important applications. In this talk, we will present recent results on the modeling, analysis, and simulation of flows in karstic geometry. In particular, we will illustrate the derivation of single phase and two-phase models based variational principles, the mathematical validity of resulting models, and a few accurate and fast numerical algorithms for simulating the models.